I don't see the Republican party lasting too much longer in its current form (super-religious, super white, etc.).
Therefore, I think the two party system will have to split along different lines (i.e. gay marriage will be legalized and become a non-issue... other social issues will move in that direction too)...
Republican Party = Libertarian, fiscally conservative, socially libertarian live and let live.
Democratic Party = Fiscally liberal, not socialist but moving in that direction, socially still more liberal and using the government to solve social problems.
I could actually see Republicans becoming competitive in states like New Hampshire, Maine, Connecticut, Oregon, Pennsylvania, Wisconsin, Minnesota, Michigan, Iowa again... and Democrats becoming competitive in Texas, Georgia, Arizona, etc.
I see them becoming more of a faction of the Republican party; not all "true" Republicans will have to oppose ssm in 10-20 years for instance. The population is becoming more and more socially liberal; the Republican Party could get hypothetically get away with it.
That said, by all means the evangelical wing could break off. It's not unprecedented; the Bull Moose Progressives split off from the Republicans because they truly hated the business wing, and the Greenback Labor Party split off from the Democrats for more complex reasons; but mainly because there were increasing tensions with city democrats in the late 19th century. A breakoff would be unlikely, but could definitely happen.
My opinion on the future parties:
Republicans-Largely the same as today, but with a slightly broader tent. They will find a way to change their messaging to appeal to minorities.
Democrats-Largely the same as today, but more minority dominated. Liberals complain about disagreements within their own party; well, it is only likely to get worse as America gets more diverse (hey, that rhymes).
I think Republicans for the next ten years will continue to become more extreme, culminating in a McGovernesque loss. Then, they will probably move toward the center on social issues, and POSSIBLY a little bit on economic issues.
